Finite Group DatabasebetaFinite Group Databasebeta| order | 18126 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | D53×#4294 |
| unambiguous semidirect product | C53⋊(C2×#4294) |
| derived, Hall | C19×C53 ⋊ C2×C9 |
| Hall | C53×#4294 ⋊ C2 |
| Hall | C19×D53 ⋊ C9 |
| Sylow | C53 ⋊ C2×#4294 |
| Sylow | C19 ⋊ C9×D53 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C19⋊C3×D53 |
| commutator, hypocenter | C19×C53 | C2×C9 |
| Fitting, socle, cosocle | C3×C19×C53 | C2×C3 |
| prime radical | C3×C19×D53 | C3 |
| LCS | G ▷ C19×C53 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9063 |
756 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #4294⋊#6157, D53×#4294⋊C2, #4294×#6157, … |
| maximal normal subgroup of | #4294⋊#6157, D53×#4294⋊C2, #4294×#6157, … |
| maximal quotient of | #4294×Dic53, C2×D53×#4294 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18126, 10);